Consider a $2$ player game in which player $1$ can choose A or B$.$ The game ends if he$/$she chooses A$,$ while it continues to player $2$ if he$/$she chooses B$.$ Player $2$ can then choose C or D with the game ending if C is chosen, and continuing again to player $1$ if D is chosen. Player $1$ can then choose E or F $,$ with the game ending either choice.

Model this as an extensive form game.

How many pure strategies does each player have?

Identity the subgames of this game.

Suppose that choice A gives utilities $(2,0)($i$.$e$.,2$ to player A$,0$ to player E$),$ choice C$$gives $(3,1),$ choice E gives $(0,0),$ and F gives $(1,2).$ Then what are the pure Nash equilibria of the game? What SPNE outcome$($s$)$ do you obtain through backwards induction?